simplify the following expression <3

Answer:

14d + 21 = 7(2d + 3)

16 + 4w = 2(2w + 8)

Step-by-step explanation:

14d + 21

7(2d + 3)

14d + 21

14d + 21 = 7(2d + 3)

9(5r - 2)

45r - 18

14r - 7

9(5r - 2) ≠ 14r - 7

8(69 - 9)

552 - 72

489 - 72

8(69 - 9) ≠ 489 - 72

16 + 4w

2(2w + 8)

4w + 16

16 + 4w = 2(2w + 8)

32t + 16

16(2 - t)

32 - 16t

32t + 16 ≠ 16(2 - t)

The pairs of expressions that are equivalent are 14d + 21 and 7(2d + 3) and 16 + 4w and 2(2w + 8)

To do this, we test each pair of expression.

This is done as follows

14d + 21 = 7(2d + 3)

Expand

14d + 21 = 14d + 21 --- this is true

9(5r - 2) = 14r - 7

Expand

45r - 18 = 14r - 7 --- this is false

8(69 - 9) = 489 - 72

Expand

552 - 72 = 489 - 72 --- this is false

16 + 4w = 2(2w + 8)

Expand

16 + 4w = 4w + 16 ---- this is true

32t + 16 = 16(2 – t)

Expand

32t + 16 = 32 - 16t --- this is false

Hence, the pairs of expressions that are equivalent are 14d + 21 and 7(2d + 3) and 16 + 4w and 2(2w + 8)

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Answer:

that's right B) 3 - √3i

Step-by-step explanation:

(12 - √-48) / 4 =

12/4 - √-48 /4

= 3 - √(-48/16)

= 3 - √-3

= 3 - √ 3i

[tex]\\ \rm\Rrightarrow \dfrac{12-\sqrt{-48}}{4}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{12}{4}-\dfrac{\sqrt{48}i}{4}[/tex]

[tex]\\ \rm\Rrightarrow 3-4\sqrt{3}i/4[/tex]

[tex]\\ \rm\Rrightarrow 3-\sqrt{3}i[/tex]

Answer:

O DC = 65 and DE = 33.5

Step-by-step explanation:

DC is already given by AB

so DC is 65

DE would be BD split

DE is 33.5

Answer: O DC = 65 and DE = 33.5

Answer:

Step-by-step explanation:

Based on this information, you could conclude that the annual rainfall in Falls City is generally more than that of the annual rainfall in Rockaway Beach. This is based on the information provided since the numbers given are the mean annual rainfall. Meaning that this is the average amount of rain that falls in any given year in that specific location. Since the amount provided for Falls City is a larger number then it means it gets more rainfall than Rockaway Beach on average and would therefore be the safest conclusion that can be made.

Answer:

I hope this helps

Step-by-step explanation:

Therefore, Amber should graph the equation Y1 = X+61.

An inequality is a mathematical statement that compares two values or expressions using one of the inequality symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to). Inequalities are used to describe a range of possible values for a variable, rather than a single value. Inequalities can be solved by performing operations on both sides of the inequality symbol, just like equations. However, there are some important differences between solving equations and solving inequalities. For example, if we multiply or divide both sides of an inequality by a negative number, we need to reverse the direction of the inequality symbol.

Here,

To graph the inequality X+61- 12 < 13, we need to rearrange it to the form Y < MX + B, where Y is on the left-hand side and X is on the right-hand side. This gives:

Y < -X + 64

Now we can graph the line Y = -X + 64 and shade the region below it, since we want Y to be less than this expression.

Out of the equations given, Y1 = X+61 is the closest to the inequality we are trying to graph. However, the coefficients of X and Y are reversed, so we need to rearrange it to the desired form:

Y - X < 61

Y < X + 61

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Answer:

4x^4 + 6x^3 + 9x^2 − 4x + 3

Step-by-step explanation:

Simplify the expression. 4x^4 + 6x^3 + 9x^2 − 4x + 3

Step-by-step explanation:

Answer:

answer for this solution is 4x^4+6x^3+9x^2-4x+3

Answer:

124

Step-by-step explanation:

Have a nice day :)

Arc AC is 180º, arc BC is 56º:

[tex]180+56 +\arc{BA} = 360\implies BA = 124[/tex]

Answer:

4x^2 + 12x + 9

Step-by-step explanation:

(2x + 3)^2

it is in the form of (a + b)^2

(a + b)^2 = a^2 + 2*a*b + b^2

(2x + 3)^2

(2x)^2 + 2*2x*3 + (3)^2

4x^2 + 12x + 9

Answer:

% of unoccupied seats = 63.2 %

Step-by-step explanation:

Total seats = 80, 000

VIP seats = 12 % of 80, 000

              [tex]= \frac{12}{100} \times 80000\\\\= 9600[/tex]

General Seats = 39040

Remaining seats = 80000 - 9600 - 39040 = 50, 560

Percentage of un-occupied seats,

                                                 [tex]= \frac{50560}{80000} \times 100 = 63.2 \%[/tex]

Answer:

THE NUMBER OF SEATS OCCUPIED BY VIPS=80000×12/100

=9600

occupied seats=9600+39040

=48640

number of unoccupied seats=80000-48640

=31360

percentage of unoccupied seats=31360/80000×100%

=39.2%

Answer:

A coordinate plane with a horizontal line passing through (negative 4, negative 3), (0, negative 3) and (4, negative 3).

Step-by-step explanation:

Ax + By = C, where A = 0, B is positive, and C is negative

By= C or y= C/B which is negative

Since A is zero and C is negative, the line is parallel to x- axis and has negative value for y, so it is a horizontal line below zero

---------------

A coordinate plane with a vertical line passing through (1, negative 4), (1, 0) and (1, 4).

no, the line is horizontal

A coordinate plane with a vertical line passing through (negative 2, negative 4), (negative 2, 0) and (negative 2, 4).

no, the line is horizontal

A coordinate plane with a horizontal line passing through (negative 4, 4), (0, 4) and (negative 4, 4).

no, the y-values should be negative

A coordinate plane with a horizontal line passing through (negative 4, negative 3), (0, negative 3) and (4, negative 3).

yes, this is horizontal line below zero

Answer:

D

Step-by-step explanation:

Answer:

Total depreciation now will be $51500 and the depreciation for you will be $5575

Step-by-step explanation:

Your welcome! :)

Answer:

its x^2 -25

Step-by-step explanation:

simply we know,

a^2-b^2=(a-b)(a+b)

Answer:

X=0

Y=2

Step-by-step explanation:

Just finished and i got it right

[tex]\sf{3. \ \ Given : \dfrac{2}{3} - \dfrac{5}{4} + \dfrac{7}{2}}[/tex]

Let us solve the first two fractions : The LCM of 3 and 4 is 12

[tex]\sf{\implies \dfrac{4(2) - 5(3)}{12} + \dfrac{7}{2}}[/tex]

[tex]\sf{\implies \dfrac{8 - 15}{12} + \dfrac{7}{2}}[/tex]

[tex]\sf{\implies \dfrac{-7}{12} + \dfrac{7}{2}}[/tex]

LCM of 2 and 12 is 12

[tex]\sf{\implies \dfrac{-7 + 7(6) }{12}}[/tex]

[tex]\sf{\implies \dfrac{-7 + 42}{12}}[/tex]

[tex]\sf{\implies \dfrac{35}{12}}[/tex]

[tex]\sf{\implies 2 +\dfrac{11}{12}}[/tex]

[tex]\sf{\implies 2 \dfrac{11}{12}}[/tex]

---------------------------------------------------------------------------------------

[tex]\sf{4. \ \ Given : \dfrac{(2 - 7)^2 + 5}{3}}[/tex]

[tex]\sf{\implies \dfrac{(-5)^2 + 5}{3}}[/tex]

[tex]\sf{\implies \dfrac{25 + 5}{3}}[/tex]

[tex]\sf{\implies \dfrac{30}{3}}[/tex]

[tex]\sf{\implies 10}[/tex]

Answer:

2/3-5/4+7/2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The function that is  shown in the graph is strictly decreasing

"A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function."

The given function has a value of (- 5) at a certain point.

After that the function is decreased to a value of (- 10).

Therefore, we can conclude that the function is strictly decreasing.

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Answer:

9^8

Step-by-step explanation:

9²•9⁶​ = 9^(2+6) = 9^8

Answer:

IF the 6 is negative : [tex]9^{2}[/tex] · [tex]9^{-6}[/tex] then the answer is 1/[tex]9^{4}[/tex]

If the 6 is positive then the answer is [tex]9^{8}[/tex]

Step-by-step explanation:

Exponents are add when their bases are similar.

Answer:

A

Step-by-step explanation:

Answer:

option a and b

Step-by-step explanation:

peanuts=1/4 cup    ratio=1:4

raisins=1/2 cup        ratio=1:2

chocolate chips=3/4 cup      ration=3:4

granola =1 cup            ration=1:1

a. ratio of cop of rasins to cup of peanuts=2:1 or 2/1

1/2 = 1/4=2/1

do cross multiplication

4*1=2*1=2/1

4/2=2/

2/1=2/1

2:1=2:1  this is satisfied

b.ratio of cup of granola to cup of peanuts=1:4 or 1/4

1/1=1/4

do crss multiplication

1*1/4*1=1/4

1/4=1/4

1:4=1:4      this is satisfied as both are equal

c.the ratio of cup of chocolate chips to cup of raisins=3:1 or 3/1

3/4=1/2

do cross multiplication

3*2=4*1=3/1

6/4=3/1

6:4=3:1   this is not satisfied as they are different.

d.the ratio of cup of raisins to cup of granola=1:3 or 1/3

1/2=1/1

do cross multiplication

1*1=2*1=1/3

1/2=1/3

1:2=1:3    this is not satisfied as they are different.

e. the ratio of cup of granola to cup of chocolate chips =4:3 or 4/3

1/1=3/4

do cross multiplication

3*1=4*1=4/3

3/4=4/3

3:4=4:3    this is not satisfied as they are not equal

therefore ur answer is option a and b.

Answer:

the answer is D.

Step-by-step explanation:

well, the y-intercept for f(x) is at  

as you can see from the slope-intercept form is at 4, and it has an slope of 2/3.

for g(x), well an y-intercept is when x = 0, what is it from that table?  well, is at 0,3, so when x = 0, y = 3, so no dice on that one.

c)

whenever an x-intercept occurs, y = 0, for f(x) that's at  

what about the x-intercept for g(x)?  well, let's check, when is y = 0?  aha!  at -9, 0, so when y = 0, x = -9, so no dice on that one either.

d)

well, what is the slope of g(x) anyway?  well, let's pick two points off the table to get it hmmm the first two let's use,

and from a), using the slope-intercept form, we know f(x) has a slope of 2/3.

well, 2/3 is larger than 1/3, so no dice.

b)

well, you already know.

Answer:

BCA is obtuse

Step-by-step explanation:

BCA = 98 degrees

greater than 0 to less than 90 is acute angles

90 - right angle

greater than 90 to less than 180 is obtuse

98 is obtuse

Answer:

on the x axis because it is reflected there

Answer:

y= -3/2

Step-by-step explanation:

........................

Answer:

7

Step-by-step explanation:

Step-by-step explanation:  

AB//CD (Opposite sides of parallelogram are parallel)  

Angle A + Angle B = 180 (Sum of interior angles=180)  

179 + 3x - 20 = 180  

3x - 20 = 180 - 179

3x - 20 = 1

3x = 1 + 20

3x = 21

x = 21/3  

x = 7

Answer:

hope this will help u

Step-by-step explanation:

⇒  Given zeros are α=2 and β=−6.

⇒  Sum of zeros =α+β=2+(−6)=−4

⇒  Product of zeros =α×β=2×(−6)=−12

⇒  Quadratic polynomial =x  

2

−(α+β)x+(α×β)

⇒  Quadratic polynomial =x  

2

−(−4)x+(−12)

∴   Quadratic polynomial =x  

2

+4x−12

The quadratic function having 2 and -6 as zeros is f(x) = x² + 4x - 12.

Given the parameters:
Zeros of the function: 2 and -6.

To find the quadratic function f(x) with zeros at 2 and -6, first set up the equation:

x = 2 and x = -6

These are the real solutions to the quadratic equation:

This means that; ( x - 2 ) and ( x + 6 ) are the factors of the quadratic equation:

Hence:

( x - 2 )( x + 6 ) = 0

Expand using distributive property:

x( x + 6 ) - 2(x + 6 )  = 0

x² + 6x - 2x - 12 = 0

Collect and add like terms:

x² + 4x - 12 = 0

Therefore, the function will be:
f(x) = x² + 4x - 12.

The quadratic function is f(x) = x² + 4x - 12.

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

When p and q are roots, (x -p) and (x -q) are factors. The quadratic equation is then ...

  0 = (x -p)(x -q) = x^2 -(p+q)x +pq

That is, the constant term is the product of the roots and the linear term coefficient is the opposite of the sum of the roots.

Using the given sum and product, the equation can be written ...

  0 = x^2 -(-5/4)x +3/4

Multiplying by -8 gives ...

  0 = -8x^2 -10x -6 . . . . . matches lower right choice

_____

Check

The product of roots is positive, so both roots have the same sign. The sum of roots is negative, so both roots are negative. That means there are no positive real roots to the equation. Descartes' Rule of Signs tells you this means the sequence of coefficients has no sign changes. Only the choice shown below has no sign changes. All of the others have at least 1 sign change.

Answer:

the last option is coorect

Answer: 86 degrees

Step-by-step explanation:

Answer:

x= 5 , y = 34

Step-by-step explanation:

8x-6=5x+9

3x-6=9

3x=15

x=5

-

8(x5) - 6 =

34

25(x5) +9 =

34

Answer:

x = 5 and y = 34

Step-by-step explanation:

I used substitution method and did this ;

8x - 6 = 5x + 9 .....put like terms together

8x - 5x = 9 + 6

3x = 15

x = 5

y = 8 (5) - 6

y = 40 - 6

y = 34

Answer:

1/17

Step-by-step explanation:

I he had even got 1 out of the 3 places the probability would be 3/17

But as he is guessing all three places it becomes 1/17

The probability of getting the 1st,2nd, and 3rd position will be 1/17.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Given that while watching the Kentucky Derby horse races, you decide to guess who will win 1st, 2nd, and 3rd place. There are 17 horses in the race.

The probability is calculated by the formula,

Probability = Number of favorable outcomes / Number of sample

Number of favorable outcomes = 1

Number of samples = 17

Probability = Number of favorable outcomes / Number of sample

Probability = 1/17

Therefore, the probability of getting the 1st,2nd, and 3rd position will be 1/17.

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Answer:

28.7

Step-by-step explanation:

12.7% = 0.127

226 * 0.127 = 28.702

Rounded

28.7